FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach

Astley, R.J. (1996) FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach.
[in special issue: Communications in Numerical Methods in Engineering] International Journal for Numerical Methods in Biomedical Engineering, 12, (4), 257-267. (doi:10.1002/(SICI)1099-0887(199604)).

Download

Full text not available from this repository.

Description/Abstract

Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.